Towards Quantum Machine Learning with Tensor Networks

M. Fannes, B. Nachtergaele, and R. F. Werner, “Finitely correlated states on quantum spin chains,” Communications in Mathematical Physics 144

1992

Earlier work this paper cites.

Stellan Östlund and Stefan Rommer, “Thermodynamic limit of density matrix renormalization,” Phys. Rev. Lett. 75

1995

Earlier work this paper cites.

Lov K. Grover, “A fast quantum mechanical algorithm for database search,” in Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing , STOC ’96 (ACM, New York, NY, USA, 1996) pp. 212–219

1996

Earlier work this paper cites.

Peter W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM Journal on Computing 26

1997

Earlier work this paper cites.

James C Spall, “An overview of the simultaneous perturbation method for efficient optimization,” Johns Hopkins apl technical digest 19

1998

Earlier work this paper cites.

M.-B. Lepetit, M. Cousy, and G.M. Pastor, “Density-matrix renormalization study of the hubbard model [4]on a bethe lattice,” The European Physical Journal B - Condensed Matter and Complex Systems 13

2000

Earlier work this paper cites.

Guifré Vidal, “Efficient classical simulation of slightly entangled quantum computations,” Phys. Rev. Lett. 91

2003

Earlier work this paper cites.

M.B. Hastings, “An area law for one-dimensional quantum systems,” J. Stat. Mech. 2007

2007

Earlier work this paper cites.

F. Verstraete, V. Murg, and J. I. Cirac, “Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems,” Advances in Physics 57

2008

Earlier work this paper cites.

G. Vidal, “Class of quantum many-body states that can be efficiently simulated,” Phys. Rev. Lett. 101

2008

Earlier work this paper cites.

L. Tagliacozzo, G. Evenbly, and G. Vidal, “Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law,” Phys. Rev. B 80

2009

Earlier work this paper cites.

W. Hackbusch and S. Kühn, “A new scheme for the tensor representation,” Journal of Fourier Analysis and Applications 15

2009

Earlier work this paper cites.

U. Schollwöck, “The density-matrix renormalization group in the age of matrix product states,” Annals of Physics 326

2011

Earlier work this paper cites.

G. Evenbly and G. Vidal, “Tensor network states and geometry,” Journal of Statistical Physics 145

2011

Earlier work this paper cites.

Martin Schwarz, Kristan Temme, and Frank Verstraete, “Preparing projected entangled pair states on a quantum computer,” Phys. Rev. Lett. 108

2012

Cited alongside, same era.

Martin Schwarz, Kristan Temme, Frank Verstraete, David Perez-Garcia, and Toby S. Cubitt, “Preparing topological projected entangled pair states on a quantum computer,” Phys. Rev. A 88

Original

2013

Cited alongside, same era.

Roman Orus, “A practical introduction to tensor networks: Matrix product states and projected entangled pair states,” Annals of Physics 349

2014

Cited alongside, same era.

Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J. Love, Alán Aspuru-Guzik, and Jeremy L. O’Brien, “A variational eigenvalue solver on a photonic quantum processor,” Nature Communications 5

2014

Cited alongside, same era.

Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, “A quantum approximate optimization algorithm,” arxiv:1411.4028 (2014)

Valentin Khrulkov, Alexander Novikov, and Ivan Oseledets, “Expressive power of recurrent neural networks,” arxiv:1711.00811 (2017)

Original

2017

Later among the works it cites.

Zhao-Yu Han, Jun Wang, Heng Fan, Lei Wang, and Pan Zhang, “Unsupervised generative modeling using matrix product states,” arxiv:1709.01662 (2017)

Original

2017

Later among the works it cites.

Xun Gao, Zhengyu Zhang, and Luming Duan, “An efficient quantum algorithm for generative machine learning,” arxiv:1711.02038 (2017)

Original

2017

Later among the works it cites.

Isaac H. Kim and Brian Swingle, “Robust entanglement renormalization on a noisy quantum computer,” arxiv:1711.07500 (2017)

Original

2017

Later among the works it cites.

E.M. Stoudenmire, “Learning relevant features of data with multi-scale tensor networks,” arxiv:1801.00315 (2018)